The research methods employed to accomplish the stated goals are described in depth in this section. The methodology describes the study area and load characteristics, the hybrid renewable energy systems that are analysed and their component modelling, the optimisation technique, the evaluation of the objective functions, the techno-economic aspects of the system, and the suggested energy and storage management framework.

The study was conducted at the Rwamagana Industrial Park, which is part of the eastern network that includes the districts of Nyagatare, Kayonza, Ngoma, Kirehe, Gatsibo, and Rwamagana. The coordinates of this location are 30.4386˚E and 1.9535˚S. A Rwamagana feeder with a conductor size of ACSR 70/12 mm², a maximum power capacity of 12.05 MW, and a peak output of 2.2 MW supplies the research area. A 110/15 kV, 10 MVA power transformer steps down the 110 kV voltage level.

Critical projects that need sufficient electricity to run enterprises, such as irrigation, milk collection centres, mining, and special economic zones in the districts of Nyagatare and Rwamagana, are being carried out in the study region as shown in Figure 2 . Hourly demand fluctuated significantly during the year, as was to be expected. With the exception of blackouts, the lowest recorded load was roughly 1.45 kW, while the highest recorded load was 2.5 kW. As seen in Figure 3 , the connected load consistently stays rather high between 18:00 and 21:00, peaking at about 19:00 ( Figure 4 ).

This section outlines the topology of connected rooftop PV networked microgrids (NMG) examined in this research and discusses the modeling of different components, including PV, BESS, grid, and loads of each microgrid within the connected system.

The configuration under consideration is illustrated in Figure 5 , considering prosumers with residential, commercial, and industrial loads, respectively. Commercial and industrial structures offer ample space for a large rooftop PV array, leading to greater electricity generation capacity, while residential buildings provide less room. The electricity produced by PV meets the local load demand and, once satisfied, transmits any excess electricity to the grid. When the PV generation falls short of the demand, the grid provides the necessary electricity to meet the loads.

Three setups are assessed for their technical, economic, environmental, and social aspects to deliver electricity to the analyzed region. In this part, we address the modeling of Grid, PV, and BESS for every microgrid (MG) within a networked structure. Three scenarios are also examined, which include: Grid-PV-BESS-Load, Grid-PV-Load, and PV-BESS-Load. This suggested system can facilitate a two-way power flow with the grid, either acquiring or supplying electricity.

A) Photovoltaic Panel Modeling

The hourly power output of the photovoltaic panels, referred to as PPV (kW), is determined by Equation (1) and is influenced by solar irradiation and ambient temperature [24] [25] .

$P_{pv}=N_{pv}\times X_{pv}{f}_{pv}\times \frac{S_T}{S_{T,STC}}\times \left[1+{\alpha }_P\left(T_C-T_{C,STC}\right)\right]$ (1)

The variables relevant to this context include $N_{pv}$, which represents the total number of photovoltaic panels; $X_{pv}$, the rated power output of the PV system in kilowatts; and $f_{pv}$, the derating factor given as a percentage. $S_T$ stands for the total irradiance on the tilted PV surface, measured in kW/m²; while $S_{T,STC}$ refers to the standard solar irradiance value of 1 kW/m². The symbol ${\alpha }_P$, represents the power temperature coefficient in percentage per degree Celsius (%/˚C). Additionally, $T_C$ is the PV cell temperature in degrees Celsius, and $T_{C,STC}$ denotes the cell temperature under normal conditions.

B) Battery Storage System Modeling

Battery storage systems function as backup energy reservoirs when the electricity generated by RE sources falls short of fulfilling the demand [26] . The batteries are recharged when the PV generator generates enough electricity to fulfill requirements and are drained when their production is inadequate to satisfy consumption needs. Consequently, they are essential for the proper operation of a hybrid system. The flowcharts in Figure 5 illustrate the equations that depict battery functioning (both charging and discharging), where it is incorporated. [27] indicate that the subsequent restrictions influence the manner in which the battery’s energy may be stored:

$\{\begin{array}{l}{E}_{b,\min }\le E_b\left(t\right)\le E_{b,\max }\\ E_{b,\max }=N_b{E}_{b,cap}\\ E_{b,\min }=E_{b,\max }\left(1-\text{DOD}\right)\end{array}$ (2)

Here, $N_b$ denotes the total number of batteries, $E_{b,\max }$ (kWh) signifies the highest necessary storage battery capacity, $E_{b,\min }$ (kWh) refers to the minimum permissible storage battery capacity, and $E_{b,cap}$ represents the battery’s nominal capacity (kWh). DOD indicates the depth to which the battery has been discharged.

C) Inverter Modeling

As stated in [28] , Equation (3) specifies the dimensions of the inverter ( $P_{inv}$) in a hybrid RE setup. [29] clarified this equation, indicating that the inverter needs to possess a capacity 8% - 10% greater than the power demand for assuring safety.

$P_{inv}=\frac{P_{peak}}{{\mu }_{inv}}$ (3)

D) Grid Modeling

The national grid delivers interrupted electricity to the system. When the PV-Wind-BES system does not have enough power to meet demand, this equation calculates the electricity received from the grid [30] .

$P_g=P_l\left(t\right)-\left\{P_{pv}\left(t\right)+P_w\left(t\right)+P_b\left(t\right)\right\}$ (4)

where $P_g$, $P_l\left(t\right)$, $P_{pv}\left(t\right)$, $P_w\left(t\right)$, $P_b\left(t\right)$ are the power compensated by the grid, load connected, PV-module output power, wind turbine’s generated power (kW), and power stored in BES respectively.

Energy management approaches need to be applied as the microgrid is linked to the grid. The microgrid needs to facilitate energy trading, enabling it to sell excess generation or draw energy from the grid in times of shortage. Equation (5) illustrates the approach for determining the objective function to reduce the operating costs of the interconnected microgrid. The objective function considers the expenses of the generating units.

$\min {\displaystyle {\sum }_{t=1}^{24}{C}_{MG}\left(t\right)P\left(t\right)}$ (5)

where:

$C_{MG}$ represents the expense for each generation unit.

$P\left(t\right)$ is DG-generated power.

$C_{MG}\left(t\right)$ represents the cost for each unit of controllable produced power.

$MG$ represents the produced energy for each unit and the sold power to the grid.

To effectively control the power flow and accomplish the goal function by specifying decision variables, the optimisation system must be implemented in the microgrid’s energy management relationship. The ideal power flow in this study aims to lower MG’s operating costs while increasing the utilisation of renewables. Equation (6) [31] can be used to characterise the target function for every time interval:

$\min {\displaystyle {\sum }_{t=1}^T{P}_{pv}\left(t\right)C_{pv}}+P_{storage}\left(t\right)C_{storage}+P_{grid}\left(t\right)C_{grid}$ (6)

Here, $P_{pv}$ & $P_{storage}$ denote the supplied power from PV and storage generation, respectively.

$C_{pv}$ & $C_{storage}$ denote respectively the costs related to the operation and maintenance of generated power from the PV and storage.

$C_{grid}$ denotes electricity cost from the grid during period t.

$T$ indicates the overall time of optimization, which is a daily range.

In order to address the optimisation system and its objective function, constraints must be considered. Equation (7) can be used to express the power balance constraint of the system.

${\displaystyle \sum P_{load}\left(t\right)P_{pv}\left(t\right)}-P_{storage}\left(t\right)P_{grid}=0$ (7)

where:

$P_{load}$ is the total consumed power of the microgrid.

The $P_{pv}$ & $P_{storage}$ should be capped to ensure system stability; these parameters are restricted to predetermined maximum PV and BESS values, along with upholding defined SOC’s maximum and minimum levels of BESS as outlined in Equations (8) & (9).

$\{\begin{array}{l}{P}_{pv}^{\min }\le P_{pv}\le P_{pv}^{\max }\\ P_{storage}^{\min }\le P_{storage}\le P_{storage}^{\max }\end{array}$ (8)

$\{\begin{array}{l}{\text{SOC}}_{\min }\le \text{SOC}\le {\text{SOC}}_{\max }\\ E_{storage}^{\min }\le E_{storage}\le E_{storage}^{\max }\end{array}$ (9)

where:

$E$ is the BESS capacity.

It is equally important to take into account the constraints linked to energy indicators described in Equations (11) and (12), which illustrate how the energy management in the electricity lab will result in a decrease in consumption per area and per user.

$\frac{Users}{Load}<P_{MG}$ (10)

$\frac{Area}{Load}<P_{MG}$ (11)

where:

$Users$ refer to the count of individuals operating within the microgrid.

$Load$ refers to the demand needed at the meter boundary with the utility.

$Area$ represents the covered area by the microgrid about the energy demand needed at the utility boundary meter.

The balance of the power consumption, provision, and charging process of the battery is very important in this study, while minimizing NPC and maximizing reliability. Therefore, the control and the fundamental concepts of the suggested operational strategies are outlined as follows:

A) PV-Grid-Storage-Load:

Following the maximum export power threshold ( $P_e^{\max }$), surplus energy is sent to the main grid if PV system’s power generation ( $P_{pv}$) surpasses the household’s consumption ( $P_l$).

$P_e\left(t\right)=\min \left(P_e^{\max },P_{pv}\left(t\right)-P_l\left(t\right)\right)$ (12)

$P_{pv}\left(t\right)=N_{pv}\ast P_{pv}^{rated}\left(t\right)$ (13)

The solar PV system’s inverter is used to redirect extra power if the export power exceeds the limit. The expression for the discarded energy ( $P_d$) is:

$P_d\left(t\right)=P_{pv}\left(t\right)-P_l\left(t\right)-P_e^{\max }$ (14)

B) PV-Grid-Load:

If $P_{pv}$ is below the load, then the shortage of power is acquired from the grid.

$P_i\left(t\right)=P_l\left(t\right)-P_{pv}\left(t\right)$ (15)

And then, by exporting the maximum power to the grid, the extra power of PV is dumped.

$P_d\left(t\right)=P_{pv}\left(t\right)-P_l\left(t\right)-P_e^{\max }$ (16)

C) PV‐BESS‐Load:

If the BES has charge available, it will be discharged to provide the required amount of power.

$P_b^{disch}\left(t\right)=P_l\left(t\right)-P_{pv}\left(t\right)$ (17)

If the initial condition isn’t satisfied and the leftover load does not exceed the battery’s input, then any surplus power from the PV charges the battery:

$P_b^{ch}\left(t\right)=P_{pv}\left(t\right)-P_l\left(t\right)$ (18)

The below equations used to determine the battery’s SOC level and available input and output power restrictions at each time interval:

$P_b^{in}\left(t\right)=\min \left(P_b^{\max },\left(E_b/\Delta t\right)\ast \left({\text{SOC}}_b^{\max }-{\text{SOC}}_b\left(t\right)\right)\right)$ (19)

$P_b^{out}\left(t\right)=\min \left(P_b^{\max },\left(E_b/\Delta t\right)\ast \left({\text{SOC}}_b\left(t\right)-{\text{SOC}}_b^{\min }\right)\right)$ (20)

${\text{SOC}}_b\left(t+\Delta t\right)={\text{SOC}}_b\left(t\right)+\frac{P_b^{ch}\left(t\right)\ast {\eta }_b^{ch}-\frac{P_b^{disch}\left(t\right)}{{\eta }_b^{disch}}}{\frac{E_b^{\max }}{\Delta t}}$ (21)

Three configurations of the hybrid system (PV-Grid-Storage, PV-Grid, and PV-BESS) will be evaluated techno-economically, environmentally, and socially in this study using MOPSO, a heuristic method modelled after the social dynamics

of a flock of birds [32] . This is a straightforward approach that depends on the populace. Every particle in PSO represents a possible fix for the issue at hand. To get the best results, the particles in PSO move around in the high-dimensional search space and change their positions. In PSO, every particle is linked to both its own optimal location and the overall optimal position for all particles. The trajectory of these particles depends on each particle’s velocity, influenced by its own best performance, highest performance of others, reflecting the individual travel experience of the particle and the experiences of neighboring particles [33] . MOPSO replaces PSO for Single Objective Functions: Unlike PSO, in which all objective functions share a common neighborhood, MOPSO allows each function to keep its distinct area for position updates. The update for velocity in MOPSO is presented in Equation (22). The mutation operator is utilized to enhance the diversity of the quest to achieve the ideal solution.

The particles that perform best for each objective function are kept in an external archive known as the repository (REP)

$v_i^t=w\ast v_i^{t-1}+c_1\ast rand\left(\right)\ast \left(x_{Pbes{t}_i}-x_i^t\right)+c_2\ast Rand\left(\right)\ast \left({\text{REP}}_{\left(h\right)}-x_i^t\right)$. (22)

The value ${\text{REP}}_{\left(h\right)}$ is taken from the repository. Figure 6 illustrates the detailed process for minimising the AEC and LPSP problems as employing MOPSO.

The following equations illustrate the design limitations of the optimization issue:

$0\le P_{pv}\left(t\right)\le P_{pv}^{\max }$ (23)

$0\le P_{storage}^{ch}\left(t\right),P_{storage}^{disch}\left(t\right)\le P_{storage}^{\max }$ (24)

${\text{SOC}}_{storage}^{\min }\le {\text{SOC}}_{storage}\left(t\right)\le {\text{SOC}}_{storage}^{\max }$ (25)

$P_{pv}\left(t\right)+P_{storage}\left(t\right)+P_{imp}\left(t\right)-P_{exp}\left(t\right)\ge P_d\left(t\right)$ (26)

$0\le P_{exp}\left(t\right)\le P_{exp}^{\max }$ (27)

Equations (23)-(27) represent the power limitations of the PV and BES, respectively. It is important to note that the house’s load cannot be controlled. The battery’s SOC constraints are specified by Equations (24) and (25), respectively. Equation (26) represents the balance constraint, while Equation (27) indicates exported power limitation from the house’s solar PV system to main grid. The restrictions must be applicable for the overall “t”, which is 8760 hours. Pe represents the power that is exported,

Various distinct domain characteristics are used as the basis for selecting the best MG. NPC and COE factors are examined in the economic evaluation. The technical requirements address the unmet load (UL), excess or surplus energy (EE), size, and renewable dispersion (RD). CO₂ as an environmental element is also assessed. Social analysis assesses acceptance in the community and human progress. When assessing reliability, both availability index and loss of power supply probability abbreviated as AI and LPSP, respectively, are estimated. While COE and NPC are lowered in the economic side, CO and APM are environmentally reduced, and for reliability, the LPSP is decreased.

The quantity of energy produced by RES consumed in the MG is determined by the RD factor. This is how RD is computed [31] :

$\text{RD}=\left(1-\frac{{\displaystyle \sum P_{DG}}}{{\displaystyle \sum P_{pv}}+P_b}\right)\times 100$ (28)

The annual unfulfilled load divided by the total annual load is known as the UL. This is how UL is determined [34]

$\text{UL}=\frac{\text{Yearly unfulfilled load}}{\text{Total yearly load}}$ (29)

The further generated energy by the system that is not promptly utilized by connected loads referred as EE in an MG system. Batteries may be used to store this energy, or the energy may be handled by the dump load. EE should be kept to a minimum. This is how EE is computed [31] [34] with values in Table 1 .

$\text{EE}=\frac{{{\displaystyle \sum }}_{t=1}^{8760}\left(P_{pv}\left(t\right)+P_b\left(t\right)+P_{bMG}-P_l\left(t\right)x\Delta t\right)}{{{\displaystyle \sum }}_{t=1}^{8760}\left(P_{pv}\left(t\right)+P_b\left(t\right)+P_{bMG}+P_{DG}\left(t\right)x\Delta t\right)}$ (30)

1) System Self-Sufficiency Index (SSSI)

This criterion evaluates the energy of the system that needs to be fulfilled through its power production instead of depending on external sources like grid electricity. A higher level of SSSI shows increased independence and decreased reliance on outside energy sources. The SSSI measures the percentage of energy coming from RES compared to the overall load demand during a period T [35] [36] , as shown in Equation (31). This index can assess the efficiency of multi-energy systems or net-zero energy systems that rely solely on renewable energy sources. Can convert electricity into different forms of energy to meet different energy needs. Additionally, the SSSI can predict energy security and reductions in greenhouse gas emissions.

$\text{SSSI}=\frac{{\displaystyle {\int }_0^T\min \left\{P_l\left(t\right),P_T\left(t\right)\right\}\text{d}t}}{{\displaystyle {\int }_0^T{P}_l\left(t\right)\text{d}t}}$ (31)

2) System Self-Consumption Index (SSCI)

The SSCI evaluates the quantity of energy generated by RES that is utilized internally to fulfil energy demands, instead of being sent back to the grid [37] . A greater Self-Sufficiency Index (SSCI) indicates increased self-reliance and reduced reliance on the electricity grid. SSCI computes the proportion of immediate electricity demand fulfilled by RES compared to the total renewable energy output during a period T [35] , as shown in Equation (32).

$\text{SSCI}=\frac{{\displaystyle {\int }_0^T\min \left\{P_l\left(t\right),P_T\left(t\right)\right\}\text{d}t}}{{\displaystyle {\int }_0^T{P}_T\left(t\right)\text{d}t}}$ (32)

The net present cost is computed as follows [38] where NPC is the total of the life’s beginning cost ( $C_{ic}$), operation and maintenance costs ( $C_{om}$), and replacement spare costs ( $C_{rsc}$).

$C_{NPC}=\frac{C_{ic}+C_{rsc}+C_{omc}}{CRF\left(i_d,t\right)}$ (33)

$C_{ic}={\displaystyle \sum N_{com}\times C_{com}};C_{com}=\text{pv},\text{inverter},\text{converter},\text{battery}\&\text{DG}$ (34)

$\begin{array}{l}{C}_{omc}={\displaystyle \sum N_{com}}\times C_{com}\times {\displaystyle {\sum }_{n=1}^{25}{\left(\frac{1+i_r}{1+r_r}\right)}^n};\\ C_{com}=\text{pv},\text{inverter},\text{converter},\text{battery}\&\text{DG}\end{array}$ (35)

The systems’ spare parts for the batteries, DG, inverter, and converter are change, Equation (36) governs the replacement spare costs:

$\begin{array}{l}{C}_{rsc}={\displaystyle \sum N_{com}\times C_{com}}\times {\displaystyle {\sum }_{n=1}^{25}\left(\frac{i_r}{{\left(1+i_r\right)}^n-1}\right)};\\ C_{com}=\text{pv},\text{inverter},\text{converter},\text{battery}\&\text{DG}\end{array}$ (36)

Equation (37) is used to get capital recovery factor [38] :

$CRF\left(i_d,t\right)=\frac{i_d{\left(1+i_d\right)}^n}{{\left(1+i_d\right)}^n-1}$ (37)

The cost of electricity per unit, or COE, is determined as follows [16] :

$C_{COE}=\frac{C_{NPC}\times CRF\left(i_d,t\right)}{365\times {\displaystyle {\sum }_{t=1}^n{P}_l\left(t\right)}}$ (38)

where $P_l$ and n are the load power at time t and the number of years, respectively; r, d, and i stand for interest, annual, and inflation rates, respectively.

In systems analysis, social influences refer to how the system affects community and its constituents. This covers elements including safety, dependability, cost-effectiveness, and energy availability. The involvement of stakeholders and the local community in the development, deployment, and supervision of MG systems is another example of a social component. The social component is essential as it guarantees that MG systems are developed then put into place to satisfy community demands and expectations while encouraging sustainable growth.

The creation and upkeep of MGs can lead to employment opportunities in a number of industries, such as engineering, building, installation, and maintenance. There will be a need for qualified experts to plan, develop, and manage these systems as the demand for MGs increases. Additionally, MGs can increase electricity to various industrial zones lacking conventional power sources, opening up employment opportunities in those areas. All things considered, the expansion of MGs can promote sustained economic growth and employment creation. In Rwanda, RESs create new work opportunities. The development of emerging nations is intimately related to expansion of RESs.

Therefore, this is how the job creation opportunity (JCO) is computed and results are presented in Table 2 [39] :

$\text{JCO}={\displaystyle \sum J{C}_{com}\times P_{com}};com=\text{pv},\text{inverter},\text{converter},\text{battery}\&\text{DG}$ (39)

where $J{C}_{com}$ is job creation and $P_{com}$ represents the maximum power of each of system’s components.

Human development index (HDI) or socioeconomic development is measured. It also has to do with the energy that people use. The HDI rises in tandem with the energy consumption. This is how the HDI is determined as [40] :

$\text{HDI}=0.09788{\log }_{\text{e}}\left[\left(E_l+\text{minimize}\left({\epsilon }_{mee}\times E_{ee}\times {\epsilon }_{ACl}\times E_l\right)\right)/N_{human}\right]-0.0310{\epsilon }_{mee}$(40)

The mechanism appears to link human development to energy-related parameters. Where $E_{ee}$ is the annual EE, ${\epsilon }_{mee}$ is the factor of EE, $E_l$ is the load energy, and ${\epsilon }_{ACl}$ is the factor of raising the AC load. where $N_{human}$ is human users’ total number of hybrid renewable-energy microgrid systems [31] . The numerator combines the baseline energy with the minimized product of efficiency factors and energy demand, then normalizes by $N_{human}$, the population. The logarithmic function smooths extreme variations, reflecting diminishing returns of energy access on HDI. This approach emphasizes the role of energy availability and efficiency in shaping human development outcomes such as enabling better access to education or health services through reliable power.

Avoided carbon dioxide (CO₂) emissions

By choosing to employ renewable energy sources (RES) rather of fossil fuels, carbon dioxide (CO₂) emissions that are forbidden from entering the atmosphere were avoided. The annual estimate of CO₂ emissions averted by switching from the conventional grid to renewable energy sources is shown in Equation (41) [41] .

${\text{Avoided}}_{{\text{CO}}_{\text{2}}}=\left({\text{SO}}_2+{\text{NO}}_{\text{x}}+{\text{CO}}_2\right)\left(0.001\right)\left({\displaystyle {\sum }_{t=1}^{8760}{P}_{load}\left(t\right)}-{\displaystyle {\sum }_{t=1}^{8760}{P}_{gs}\left(t\right)}\right)$ (41)

Using the emission factors for sulphur oxides (SO_x), nitrogen oxides (NO_x), and carbon dioxide (CO₂), as well as a conversion factor of 0.001, the total annual averted CO₂ emissions are calculated in kilogrammes. The amount of greenhouse gas emission reduction brought about by the installation of a grid-connected hybrid system is determined by Equation (42) [42] .

${\text{CO}}_2\text{Saving}\text{PV},\text{WT}=\left({\text{PV}}_{\text{kWh}}+{\text{Bat}}_{\text{kWh}}\right)\times 0.747\frac{{\text{kg CO}}_{\text{2}}}{\text{kWh}}$ (42)

The system’s overall greenhouse gas emissions are determined by multiplying the net grid electricity in kWh by emission factor for each pollutant, which is expressed in g/kWh and are presented in below Table 3 .

The reliability index is used to assess the MG’s performance. AI and LPSP are crucial dependability measures. LPSP is the shortfall in power generated and delivered to load as a result of weather and system component failure. This is how LPSP is computed [45] :

$\text{LPSP}=\frac{{\displaystyle \sum \left(P_l-P_{pv}-P_{BMG}+P_b+P_{DG}\right)}}{{\displaystyle \sum P_l}}$ (43)

$\text{AI}=1-\text{LPSP}$ (44)

In order to support the industrial area in Rwamagana, Rwanda, this study objective is to identify the energy system that offers the best overall system performance and economic efficiency for PV/Battery system. The effect of improving the assessment of economic factors like Net Present Cost (NPC) and Cost of Energy (COE) criteria, as well as social factors like Job Creation Opportunity (JCO) and the Human Development Index (HDI), on lowering technical aspects like Loss of Power Supply Probability (LPSP), will also be evaluated. The purpose of this study is to clarify how energy is spread among various setups by looking at excess energy. HDI, JCO, and NPC are additional objective functions that result from system optimisation. Equation (44) can be used to express the optimisation theory for any system that is being studied [46] .

$\{\begin{array}{l}O{F}_1=\min \left(\text{NPC},\text{COE},\text{LPSP}\right)\\ O{F}_2=\max \left(\text{HDI},\text{JCO}\right)\end{array}$ (45)

Subject to:

$\{\begin{array}{l}{N}_x^{\min }\le N_x\le N_x^{\max },x=\left\{\text{pv},\text{Batt},\text{Storage},\text{Grid}\right\}\\ 0\le \text{LPSP}\le 1\%\end{array}$ (46)

The number of components that make up the proposed systems is denoted by $N_x$.

Figure 7 illustrates the convergence of the PSO algorithm in optimizing load demand for a grid-connected system in the study area.

The scatter plot illustrates the relationship between the Loss of Power Supply Probability, (expressed in percentage) and the Annualized System Cost. As observed in Figure 7 , there is a clear inverse relationship: as LPSP increases, indicating a higher probability of power supply shortfalls, the ASC decreases. This trend suggests that achieving higher reliability (lower LPSP) comes at a greater financial cost, whereas allowing for more frequent power shortages reduces system expenses. The data points, represented by red open circles, form a relatively smooth downward curve, emphasizing the trade-off between system reliability and cost. This analysis is crucial in designing hybrid renewable energy systems, where decision-makers must balance reliability with economic feasibility.

In this subtopic, we present a detailed analysis of the technical, economic, environmental and social criteria results obtained from the study as presented in Table 4 on the optimal integration and performance of Rwanda’s electrical network with high penetration of interconnected PV rooftop microgrids. By evaluating these criteria, we assess the operational impacts and benefits of widespread PV deployment on the existing grid infrastructure in the study Rwamagana area.

The obtained technical results demonstrate a well-performing energy system with promising reliability and efficiency indicators, such as SSSI of 0.4186, and SSCI of 0.3088 reflects a reasonable ability of the system to meet energy demands.

These evaluation criteria provide crucial insights into the feasibility, stability, and efficiency of transitioning towards a more decentralized and renewable-powered network in Rwanda and shows the analysis and assessment of best outcomes in the area under study, including the optimum results for technical, economic, and environmental factors.

The system produced an excess energy amount of 3568803.59 kWh, indicating a surplus that could potentially be stored or sold to the grid. Importantly, the unmet load is zero, highlighting that the system successfully met all the required demand without shortages. The LPSP is very low at 0.0096, further emphasizing the system’s high reliability. Additionally, the total energy transfer reached 3913515.11 kWh, confirming the system’s capability to generate and deliver a substantial amount of energy. Overall, these results suggest a technically strong and reliable energy system with opportunities for optimizing energy excess management.

Figure 8 displays the power profiles of system load, battery output energy, and solar generation over approximately 180 hours. The load (blue dashed line) remains relatively stable around 2000 kW, indicating consistent energy demand. Solar power (green line) shows high variability with sharp peaks reaching up to nearly 14,000 kW, highlighting intermittent nature of solar energy input. The battery output (orange line) appears to respond dynamically, providing power during periods of low solar generation and reducing output or charging during high solar availability. This interplay suggests an effective energy management strategy where the battery compensates for solar fluctuations to ensure a stable power supply that meets the load demand.

Figure 9 illustrates the variation in power over approximately 180 hours, comparing system Load, Battery Charging Load, and Solar Power (SolPower). The dashed blue line represents the constant or mildly fluctuating Load, which remains relatively steady around 2000 kW. In contrast, the red line indicates Battery Charging Load, which shows intermittent charging patterns aligning closely with the availability of solar power. The green line representing SolPower displays a highly variable and peaky profile, with solar generation reaching values above 12,000 kW during sunny intervals. These peaks in SolPower correspond with spikes in Battery Charging Load, demonstrating a strategy of charging batteries primarily when solar energy is abundant, thus enhancing renewable energy utilization.

The chart visualizes the power distribution over time (in hours), highlighting three key parameters: Grid Import, Load, and Solar Power Output (Psol). The left Y-axis (blue) represents power in kilowatts (kW), while the right Y-axis (orange) corresponds to the normalized scale of solar power output. The magenta-filled area indicates the electrical load, the dashed line shows the Grid Import, and the black dash-dot line represents solar power generation. The plot shows a fluctuating solar output peaking periodically, while the grid import and load remain relatively stable, indicating reliance on grid supply when solar output is insufficient. ( Figure 11 ).

Figure 12 presents the annual power exchange with the grid, showing both grid purchases (blue) and grid sales (orange) across time in hours. The y-axis represents kilowatts (kW) power, while the x-axis spans an entire year (up to 8760 hours). The data illustrates that for the majority of the year, there is a high frequency of grid sales, indicating surplus power, likely from renewable generation such as solar, being exported. Conversely, grid purchases are concentrated in certain periods, likely correlating with times of low renewable generation or high demand. The sporadic and uneven distribution highlights the variability in power flows typical in systems with high renewable energy penetration.

The economic analysis of the system indicates strong financial viability based on the obtained criteria. The LCOE is notably low at 0.04 $/kWh, suggesting cost-effective energy production. The Net Present Cost is calculated at $8867793.27, reflecting the total cost of the project over its lifetime ( Table 5 ).

The payback period is estimated at 9.6 years, meaning the project will recover its initial investment within a reasonable timeframe. The annual operating cost stands at $758129.28, with a significant contribution from solar energy at $730313.90. The grid component contributes a small negative cost of −$15005.35, likely due to energy export revenues or net metering benefits. Battery storage and inverter systems incur additional costs of $41613.49 and $1207.24, respectively. Overall, the results demonstrate that the system is economically attractive, primarily driven by affordable solar energy costs and supported by modest storage and inverter expenses.

The bar chart in Figure 12 illustrates the annualized cost of various energy system components—Battery, Inverter, Solar, and Grid—in USD. It is evident that the Solar component dominates the cost distribution, contributing over $700,000 annually, which likely reflects high initial capital investment and large system size.

The Battery system follows, though at a much lower cost, indicating a moderate storage requirement. The Inverter cost is negligible, possibly due to system design or integration efficiencies. Interestingly, the Grid cost appears slightly negative, potentially suggesting revenue from grid exports or avoided grid purchases, highlighting the system’s economic interaction with external electricity networks ( Figure 13 ).

In this study, the environmental impact was assessed using two key criteria: avoided CO₂ emissions and renewable energy penetration. The results demonstrate a significant positive outcome, with a total of 10374932.8 kilograms of CO₂ emissions avoided, highlighting the substantial reduction in greenhouse gas emissions achieved through the proposed system ( Figure 14 ).

Furthermore, the renewable energy penetration reached an impressive 97.75%, indicating that nearly the entire energy demand was met through renewable sources. Together, these results underscore the effectiveness of the system in promoting sustainability, reducing reliance on fossil fuels, and contributing meaningfully to climate change mitigation efforts. The monthly energy distribution chart showcases the interplay between various power sources—solar, battery output, and grid (import/export)—and the corresponding load demand throughout the year. Solar energy, represented by the dominant blue bars, consistently contributes the majority of the power, peaking in July due to higher solar irradiance. Battery output and grid import supplement the system, particularly during periods of reduced solar output. Notably, grid export is more prominent in months with excess solar generation, indicating efficient energy utilization and potential economic benefits. The load curve (blue line) remains relatively stable, emphasizing the system’s need to adapt to seasonal variations in solar availability.

The values for the social criteria achieved during the optimization of the proposed systems, using the implemented algorithms, are presented in Table 3 . In this study, three social criteria were considered: Human Development Index (HDI), job creation opportunities (JCO), and social acceptance. This work is among few studies that assess these social factors within Rwandan context.

Based on simulation results, each system is expected to generate three (3) direct jobs and contribute to improving the HDI. Regarding the third social criterion, social acceptance, we referred to field survey conducted [47] the field survey carried out by on accessibility to renewable energies in SSA and 95% of the surveyed individuals expressed positive attitudes toward adopting or transitioning to RE systems.